A major problem in modeling of turbulent supersonic flows is the correct assessment of viscous-inviscid interaction problems. Of particular interest is the interaction of boundary layers with shocks. Present turbulence models give in most cases unsatisfactory results in the region of rapid distortion and in the separation region (if one is present) in particular with regard to mean flow profiles and turbulence quantities. The objective of the present work is the direct numerical simulation of shock boundary layer interaction. This report summarizes the first phase during which a numerical method suitable for this problem has been developed and a computer code has been written and tested.